RR Lyrae stars in Galactic globular clusters.III. Pulsational predictions for metal content Z=0.0001 to Z=0.006

The results of nonlinear, convective models of RR Lyrae pulsators with metal content Z=0.0001 to 0.006 are discussed and several predicted relations connecting pulsational (period and amplitude of pulsation) and evolutionary parameters (mass, absolute magnitude and color of the pulsator) are derived. These relations, when linked with the average mass of RR Lyrae stars, as suggested by horizontal branch evolutionary models, provide a ``pulsational'' route to the determination of the distance modulus, both apparent and intrinsic, of RR Lyrae rich globular clusters. Based on a preliminary set of synthetic horizontal branch simulations, we compare the predicted relations with observed variables in selected globular clusters (M2, M3, M5, M15, M55, M68, NGC 1851, NGC 3201, NGC 5466, NGC 6362, NGC 6934 and IC 4499). We show that the distance moduli inferred by the various theoretical relations are mutually consistent within the errors, provided that the value of the mixing-length parameter slightly increases from the blue to the red edge of the pulsation region. Moreover, we show that the relative ``pulsational'' distance moduli fit well previous empirical results and that the parallax of the prototype variable RR Lyr, as inferred by the predicted Period-Wasenheit relation, is in close agreement with the HST astrometric measurement